tag:blogger.com,1999:blog-5446791900286151647.post7670202938335571918..comments2012-04-01T14:11:57.067-07:00Comments on Soap bubble geometry: Summary (packings)Simon Coxhttp://www.blogger.com/profile/15761018190205756689noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-5446791900286151647.post-52027989315273091932012-04-01T14:11:57.067-07:002012-04-01T14:11:57.067-07:00For bidisperse packings a stronger question whethe...For bidisperse packings a stronger question whether area fraction increases as the area ratio increases from 0 to 1. There is an analogous question for bidisperse partitions, namely whether the perimeter increases as the area ratio increases from 0 to 1 (fixing the sums of the areas). Work of Fortes and Teixeira [FT] indicates that it does, although the perimeter function graphed in their paper should be divided by sqrt(1+lambda) for normalization to fixed sum of areas. If the 6_1 6_1 structure is replaced by disjoint phases of hexagons then the perimeter looks strictly increasing.<br /><br />[FT] M. A. Fortes and P. I. C. Teixeira, Minimum perimeter partitions of the plane into equal numbers of regions of two different areas, Eur. Phys. J. E 6 (2001), 133–137.Frank Morganhttps://www.blogger.com/profile/15570207935455948782noreply@blogger.com